This is kind of a comp sci question, but I figured I could use some input from FFT experts.
I've already got a radix-4 cooley-tukey implementation of the NTT briefly described on page 9-10 of https://who.rocq.inria.fr/Gaetan.Leurent/files/SIMD.pdf
which was pretty convenient when it came to putting together an Sse2 implementation (parallel computations of 4 32-bit unsigned integers instead of 1 at a time).
In the interest of squeezing out every last bit of efficiency for repeated runs, however, should I consider an alternate FFT implementation (Bruun's algorithm, for instance)? If you need more context to answer this, I'll be happy to provide more, this is the first time I've ever had to implement an FFT and I'm not sure what information is important. I'd also appreciate any further explanation you can provide; my understanding is still pretty shallow.